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3 years ago

What is the rate of change and initial value for the linear relation that includes the points shown in the table?

Mathematics

2 answers:

Wittaler [7]3 years ago

7 0

Answer:

Initial value $12$ , rate of change: $-2$

Step-by-step explanation:

Step 1

Find the rate of change

we know that

In a linear equation the rate of change is equal to the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

$A(1,10)\ B(2,8)$

Substitute the values

$m=\frac{8-10}{2-1}$

$m=-2$ ----> rate of change

Step 2

Find the initial value

The equation of the line into slope-point form is equal to

$y-y1=m(x-x1)$

Substitute

$y-10=-2(x-1)$

$y=-2x+2+10$ $y=-2x+12$

The initial value is the value of y when the value of x is equal to zero (is the y-intercept)

$y=-2*0+12=12$ ----> initial value

sleet_krkn [62]3 years ago

3 0

Answer:

Step-by-step explanation:

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Which equation in point-slope form contains the point (4, –1) and has slope 3?

Andrew [12]

Answer:

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Step-by-step explanation:

Hi there!

We are given a slope of 3 and a point (4,-1).

We need to find the equation of the line in point-slope form

Point-slope form is given as y-y1=m(x-x1), where m is the slope, and (x1,y1) is a point

We have all of the needed information to substitute into the formula

First, let's label the values of everything to avoid any confusion

m=3

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now substitute into the formula *remember, the formula has SUBTRACTION, and we have a NEGATIVE number, so we'll end up subtracting a negative*

y--1=3(x-4)

simplify

y+1=3(x-4)

That's it!

Hope this helps :)

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vovangra [49]

$\frac{5}{6} h$ - $\frac{7}{12}$ = $-\frac{3}{4} h$ - $\frac{13}{6}$

First, simplify $\frac{5}{6} h$ to $\frac{5h}{6}$ / Your problem should look like: $\frac{5h}{6}$ - $\frac{7}{12}$ = $-\frac{3}{4} h$ - $\frac{13}{6}$
Second, simplify $\frac{3}{4} h$ to $\frac{3h}{4}$ / Your problem should look like: $\frac{5h}{6}$ - $\frac{7}{12}$ = $- \frac{3h}{4}$ - $\frac{13}{6}$
Third, multiply both sides by 12, which is the LCM of 6 and 4. / Your problem should look like: 10h - 7 = -9h - 26
Fourth, add 9h to both sides. / Your problem should look like: 10h - 7 + 9h = -26
Fifth, simplify 10h - 7 + 9h to 19h - 7 / Your problem should look like: 19h - 7 = -26
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Eighth, divide both sides by 19. / Your problem should look like: h = $- \frac{19}{19}$
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Answer: h = -1

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